A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix

Abstract

Abstract This paper presents an O ( n 2 ) method based on the twisted factorization for computing the Takagi vectors of an n ‐by‐ n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O ( n 2 ) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O ( n 2 ) flops. An analysis shows the accuracy and orthogonality of Takagi vectors. Also, techniques for a practical implementation of our method are proposed. Our preliminary numerical experiments have verified our analysis and demonstrated that the twisted factorization method is much more efficient than the implicit QR method, divide‐and‐conquer method and Matlab singular value decomposition subroutine with comparable accuracy. Copyright © 2009 John Wiley & Sons, Ltd.